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Abstract

A novel fabrication method of Si photonic slabs based on the selective formation of
porous silicon is reported. Free-standing square lattices of cylindrical air holes
embedded in a Si matrix can be achieved by proton beam irradiation followed by electrochemical
etching of Si wafers. The photonic band structures of these slabs show several gaps
for the two symmetry directions for reflection through the z-plane. The flexibility
of the fabrication method for tuning the frequency range of the gaps over the near-
and mid-infrared ranges is demonstrated. This tunability can be achieved by simply
adjusting the main parameters in the fabrication process such as the proton beam line
spacing, proton fluence, or anodization current density. Thus, the reported method
opens a promising route towards the fabrication of Si-based photonic slabs, with high
flexibility and compatible with the current microelectronics industry.

Keywords:

Photonic slabs; NanoPSi; Photonic band structure; Proton beam writing

Background

Since the concept of photonic crystal was proposed and theoretically discussed several
decades ago [1,2], many novel photonic devices have been proposed aiming at controlling the propagation
of electromagnetic waves. Practical applications of these results require the use
of three-dimensional (3D) photonic crystal devices with 3D band gaps [3,4]. However, the fabrication of such structures is not a simple task since they require
a complex 3D connectivity and strict alignment requirements [5]. An alternative aiming at an easier fabrication process relies on the development
of photonic crystal slabs. These are periodic two-dimensional dielectric structures
which use index guiding to confine light in the third dimension [6-8]. Photonic crystal slabs share almost of the properties with true 3D photonic crystals;
however, new issues such as slab thickness or mirror symmetries are determinant in
their optical behavior [9].

Additionally, Si-based photonic crystals are one of the most promising photonic devices
due to their easy integration in Si technology, allowing novel applications in several
fields, such as optical devices including waveguides and filters [10,11], or in the field of telecommunications, as antenna substrates or reflectors [12]. A wide variety of methods have been used to fabricate photonic crystal slabs based
on Si. Semiconductor fabrication techniques such as advanced lithography or holography
[13,14] are some of the most widely used methods. Also, nanoindentation lithography followed
by macroporous silicon formation is one of the most recently used techniques to fabricate
Si-based photonic crystals in two and three dimensions [15].

Nanostructure porous silicon (nanoPSi) is a popular material for the fabrication of
photonic devices since it shows a variety of interesting properties such as efficient
photoluminescence in the visible range at room temperature [16], tunable refractive index, or low light absorption in the visible [17]. Hence, nanoPSi has been used for the fabrication of a number of optical devices
including one- [18,19] and two-dimensional [20,21] photonic crystals. These devices allow novel applications such as bimolecular screening
[22], amplification of optical detection [23], and encoded microcarriers [24].

In the present work, a novel and highly flexible fabrication process of Si-based photonic
crystal slabs is demonstrated. This method is based on the selective formation of
nanoPSi by electrochemical etching after a proton beam with different energies and
fluences is focused on the Si wafer. This technique allows fabrication of free-standing
slabs consisting of square lattices of cylindrical air holes in a Si matrix which
can work over most of the near- and mid-infrared range. The flexibility of this technique
for tuning the frequency ranges and sizes of the photonic gaps is demonstrated and
makes this method a very promising candidate for the development of Si-based photonic
devices. On one hand, this flexibility is given by the possibility of adjusting the
lattice parameter of the structures, by changing the spacing between irradiated lines.
This is easily achievable due to the special experimental setup, which allows focusing
the proton beam down to 100 nm, permitting a course tuning of the frequency range
of the gaps. On the other hand, by adjusting the main parameters in the fabrication
process such as proton fluence or anodization current density, the radius of the air
holes and slab thickness can be modified in a very accurate way, given the possibility
of a fine tuning of the gaps.

Methods

Photonic slabs consisting of a square lattice of cylindrical air holes in a Si matrix
were fabricated in several steps as follows: First, a 250-keV proton beam was focused
down to 100 nm and scanned in both directions to define a square grid on the surface
of a p+-type Si wafer (orientation <100>; resistivity 0.02 Ω cm). For 250-keV protons, high-defect
regions are generated at a depth of 2.4 μm in bulk Si, after lines were irradiated
horizontally and vertically with moderate line fluence, as Figure 1 shows. The proton beam was provided by a nuclear microprobe at the Center for Ion
Beam Applications, National University of Singapore. Setup of this equipment allows
the control of beam line spacing and proton fluence.

In order to obtain a free-standing structure, a high-energy proton beam of 1 MeV,
which has a deeper penetration in the Si wafer with an extremely high fluence of 1 × 1012/cm, was used to define supports at the same area, as Figure 1 presents.

After the irradiation of the Si wafers, nanoPSi is selectively formed by the electrochemical
etch in HF (48%):EtOH (98%) (1:1) solutions. NanoPSi grows in low-defect regions and
unirradiated zones, whereas high-defect regions remain as Si. Due to the higher defect
density attributable to overlapped areas at the intersection of irradiated lines,
circular holes instead of square holes of nanoPSi are formed. After removal of nanoPSi
in KOH solutions, a free-standing slab of 2D square lattice of air holes is obtained,
as Figure 2 shows.

Figure 2. Scanning electron microscope image of the resulting free-standing Si-based photonic
slab. The slab is a square mesh of cylindrical air holes in a Si matrix.

An important development in Si photonic is the ability of using deep localized defects
at the end of the range of high-energy protons. This allows machining 3D Si structures
within bulk Si by selective formation of nanoPSi in the subsequent anodization process
[25,26]. As the proton beam penetrates the semiconductor, it damages the Si crystal by producing
additional vacancies [27]. Vacancy distribution produced in bulk Si depends on the energy and fluence of the
proton beam. Then, the irradiated wafer is electrochemically anodized in a dilute
HF solution as mentioned above. At moderate fluence, the buried regions of high vacancy
concentration inhibit nanoPSi formation, whereas regions with low-density vacancies
or unirradiated zones allow nanoPSi formation. Finally, nanoPSi can be removed in
KOH solutions.

Results and discussion

The optical behavior of the photonic crystal slabs was studied by determining their
characteristic photonic band structures (PBSs). PBS of these quasi-3D photonic lattices
was computed using the MPB (MIT Photonic Bands) package [28]. The computation of slab band structures requires two steps: First, the slab eigenstates
are calculated using preconditioned conjugate-gradient minimization of the Rayleigh
quotient in a plane-wave basis [29]. Second, the light cone is obtained and overlapped. As the method requires a unit
cell to compute the eigenstates, and the slab is only periodic in two dimensions,
a z-supercell approach is required, assuming a periodic sequence of slabs separated
by enough background regions. In this case, guided eigenstates are unaffected and
only no guided modes are disturbed, but since they fall inside the light cone, their
frequencies are inconsiderable [6].

Figure 3 shows a typical PBS for a square lattice of cylindrical air holes in a Si matrix.
In this case, the ratios r/a and h/a (where r is the radius of the air holes, a is the lattice parameter, and h is the thickness of the slabs) were set to 0.38 and 0.4, respectively. These parameters
correspond to the experimental ones for a fluence of 5 × 1010 proton/cm and a current density of 300 mA/cm2 (see Tables 1 and 2 for further details). The dielectric constant of Si matrix was set as ϵ = 11.56 [30].

Figure 3. Photonic band structures corresponding to a square lattice of cylindrical air holes
in a Si matrix. The ratios r/a and h/a were set as 0.38 and 0.4, respectively; the parameters correspond to a fluence of
5 × 1010/cm and a current density of 300 mA/cm2, ϵ = 11.56 being the dielectric constant of Si. (a) Slabs bands with even symmetry with respect to the z-plane (TE-like). (b) Slabs bands with odd symmetry with respect to the z-plane (TM-like).

Table 1.Experimental ratios (r/a) for the different combinations of proton fluence and applied current density (J)

Table 2.Experimental ratios (h/a) for the different combinations of proton fluence and applied current density (J)

In Figure 3a, several gaps can be observed below the light cone for bands with even symmetry
(transverse electric (TE)-like) with respect to reflections through the z-plane (z direction being the height slab direction). The first gap opens from the first band
to the second band, between 0.342 and 0.366 of the normalized frequency. The second
one appears from 0.38 to 0.47 of the normalized frequency, between the second and
third band. The last and widest gap opens from the fourth band to the fifth band,
between 0.503 and 0.617 of the normalized frequency. In this structure, a gap also
appears for bands with odd symmetry with respect to the z-plane (transverse magnetic
(TM)-like) below the light cone. This gap appears between the second and third bands
in the normalized frequency range from 0.495 to 0.535. This gap shares a range of
frequency with the third gap for the TE-like bands. So, this structure has a complete
photonic gap between 0.503 and 0.535 of the normalized frequency.

The frequency ranges where gaps are located depend on the lattice parameter of the
structure, since normalized frequency is defined as the ratio between the lattice
parameter and the wavelength (normalized frequency = a/λ). Hence, by controlling the lattice parameter, the frequency range where these structures
operate can be tuned. The fabrication process allows control of the lattice parameter
by changing the proton beam line spacing when the structure is being irradiated. Figure
4 shows several structures with different lattice parameters. In this case, the irradiated
proton lines and line spacing decreased from 3 μm (Figure 4a) to 2 μm (Figure 4b) and 1.5 μm (Figure 4c) to obtain structures with lattice parameters of 3, 2, and 1.5 μm, respectively.

Figure 4. Scanning electron microscope images of three different samples. (a) Structure with a lattice parameter of 3 μm due to the proton beam line spacing was
set to 3 μm. (b) Same structure with a lattice parameter of 2 μm. (c) The photonic slab presents a period of 1.5 μm.

Figure 5 presents the different frequency ranges of the gaps for several different lattice
parameters of the photonic slab. The theoretical results show that the frequency range
can be turned over the near-mid infrared range by changing the period of the structure
from 1 μm to 3 μm, i.e., by modifying the proton beam line spacing during the irradiation
process.

Figure 5. Theoretical frequency ranges of gaps for square lattices of cylindrical air holes
with different lattice parameters. The ratios r/a and h/a were set as 0.38 and 0.4, respectively. The dielectric constant of Si was set at
ϵ = 11.56.

Furthermore, the slabs eigenstates, and consequently their optical properties, strongly
depend on the ratios r/a and h/a. Once the frequency ranges where the structures operate are determined by fixing the
lattice parameter, a fine tuning of these frequency ranges can be accomplished by
adjusting the thickness of the slab and radius of the cylindrical air holes. These
two parameters can be set by adjusting two main factors in the fabrication process,
namely, proton fluence of the beam during the irradiation process and applied current
density in the electrochemical anodization process. To study the effect of proton
fluence and applied current density on the ratios r/a and h/a, lines with some millimeter length were irradiated on Si with different proton fluences.
Then, the irradiated areas were electrochemically anodized by applying different current
densities.

Figure 6 shows cross-sectional SEM images of buried Si cores, in which 250-keV proton beam
was used with three different line fluences: 5 × 1010/cm, 8 × 1010/cm, and 1 × 1011/cm on three different Si wafers. Then, each wafer was anodized by applying three
different current densities (3 mA/cm2, 30 mA/cm2, and 300 mA/cm2) with enough time to completely undercut the cores. As noticed in Figure 6, Si core width and core height vary according to the proton fluence and applied current
density. For square lattices of air hole slabs, the relationship between the radius
of the air holes and the core width is given by r = (a-core width)/2, whereas the slab thickness is equal to the core height: h = core height.

Tables 1 and 2 summarize the experimental values of the ratios r/a and h/a, respectively, for the different combinations of proton fluences and anodization
current densities. The higher the proton fluence, the larger the core width and core
height; thus, the ratio r/a decreases, whereas h/a increases for all of the current densities. On the other hand, for a fixed proton
fluence, the higher the applied current density, the higher the r/a and the smaller the h/a; due to increasing current density, the core width and height become smaller for
the same proton fluence.

The effect of varying the proton fluence and applied current density on the optical
properties of these structures was studied. Figure 7 shows the frequency ranges of the photonic gaps for the different experimental line
fluences and current densities, when the lattice parameter was fixed to 1.5 μm. For
a current density of 3 mA/cm2, only a TE-like gap appears between the second and third bands. The size of this
gap increases from 5% to 8% when the line fluence increases from 5 × 1010/cm to 8 × 1010/cm. However, an even higher fluence of 1 × 1011/cm only provides a 2% gap. The gap size is defined as , where ω is the normalized frequency, Δω = ωband-n − ωband-n-1, and wc is the central frequency of the gap.

Figure 7. Computed frequency ranges of the photonic gaps for different line fluences and current
densities. The frequency ranges are for a square lattice of cylindrical air holes in a Si matrix
with a fixed period of 1.5 μm.

For a current density of 30 mA/cm2, PBS shows only the same TE-like gap as before, between the second and third band.
In this case, the higher the line fluence, the smaller the gap size, being around
12% when the proton fluence is relatively low (5 × 1010/cm), decreasing to 10% while increasing fluence to 8 × 1010/cm and dropping down to 3% when fluence is further increased to 1 × 1011/cm. In these cases, TM-like gaps do not appear yet.

When the current density in the etching process is increased to 300 mA/cm2, new gaps open for both symmetries, as Figure 7 shows. For the first TE-like gap, between the first and second bands, its size is
reduced as the line fluence is raised, being more than 17% for a low fluence (5 × 1010/cm) and dropping down to 3% for the highest fluence (1 × 1011/cm). The same behavior appears on the second TE-like gap, between the second and
the third bands, showing its maximum size for a low fluence (22%) and its minimum
for the highest fluence. Also, in the third TE-like gap, between the fourth and fifth
bands, the same behavior is found. However, for the highest fluence (1 × 1011/cm), the gap disappears. Furthermore, for this current density, a TM-like gap appears
between the third and fourth bands. The size of this gap is almost constant around
8% while increasing the fluence. However, a complete gap for all the symmetries only
appears for the lowest line fluence (5 × 1010/cm).

As it can be clearly observed in Figure 7, the fabrication process allows a fine tuning of the frequency range at which the
gaps open by simply adjusting two main factors, the proton fluence during the irradiation
and applied current density in the electrochemical etch. By fixing the lattice parameter
to 1.5 μm, TE-like gaps can be turned over a large frequency range over the near-mid
infrared, from 2.4 to 6 μm. Moreover, the gap size can be modified too, allowing setting
of the frequency range where the gap opens for its proper applications. This process
can be extended to the visible and near-IR ranges by decreasing the period and using
a suitable proton fluence and applied current density.

Nevertheless, tuning the TM-like gaps is not so straightforward since they only appear
for a high current density (typically above 300 mA/cm2). However, it can also be modified by changing the proton fluence. Also, a complete
gap only appears in some special cases, but due to the flexibility of the method,
the experimental parameters can be adjusted for those special cases.

Conclusion

A highly flexible fabrication process of Si-based photonic slabs for their use as
2D photonic crystals is demonstrated. The process is based on the selective formation
of porous silicon by focusing a proton beam on a Si surface, followed by electrochemical
etching. The resulting structures are free-standing square lattices of cylindrical
air holes embedded in a Si matrix. Their photonic band structures show several gaps
below the light cone for the two main directions of symmetry for reflection through
the z-plane.

The flexibility of the presented method allows the control of the frequency ranges
where the photonic structures can operate by adjusting the proton beam line spacing
which tunes the lattice parameter of the structure. Also, a fine tuning of the frequency
range can be obtained by adjusting the proton fluence and applied current density,
which modify the radius of the air holes and thickness of the slabs. The theoretical
results suggest that the fabricated structures represent very promising candidates
for the development of Si-based photonic slabs operating in the near-mid infrared
ranges.

Competing interests

The authors declare that they have no competing interests.

Authors’ contributions

GRS carried out the theoretical studies, analyzed the results, and drafted the manuscript.
ZD carried out the fabrication process, participated in the discussion, and helped
draft the manuscript. MB assisted in the fabrication process and participated in the
discussion. VTC and RJMP helped to analyze the results and draft the manuscript. All
authors read and approved the final manuscript.

Acknowledgment

The authors acknowledge Centro de Computación Científica (Universidad Autónoma de
Madrid) for providing computational resources for numerical calculations. The authors
also gratefully acknowledge funding from Comunidad de Madrid (Spain) under project ‘Microseres’ and Ministerio de Economía y Competitividad (Spain) under research project MAT2011-28345-C02-01.